The Teaching Gap

As you will see, The Teaching Gap compares mathematics instruction in the United States, Japan, and Germany on the basis of data collected through the Third International Mathematics and Science Study (TIMSS). You might be surprised (or not) that the United States does not compare favorably. But it is important that you understand that The Teaching Gap is not about a contest. Rather it is about trying to learn more about us by examining instruction in other countries. As Stigler and Hiebert say repeatedly, mathematics instruction is a cultural phenomenon, and coming to understand one's culture is like a fish coming to understand water. An organism cannot notice its all-pervasive environment until it experiences life outside it. Our educational culture is so pervasive that there are important aspects of it that we cannot notice without experiencing cultures having aspects that differ from ours. So, please read The Teaching Gap in that spirit -- as an attempt to help us step out of our culture of mathematics teaching in order to examine it more objectively.

Reflective Essay

Please respond to these questions after reading The Teaching Gap.

1) The authors describe large variations across US, Germany and Japanese teaching cultures and little variation within cultures.

a) Describe the teaching cultures in each country and the variations that exist across the three countries.

b) Summarize the authors’ characterization of the US teaching culture. Is their characterization accurate? If not, how is it inaccurate?

2) a) Describe the major findings of the Third International Mathematics and Science Study (TIMSS).

b) Describe specific methods (see Chapter 2) that make the findings compelling. Do you believe the findings reported? If not, what flaws in the methods may invalidate the findings?

3) The authors of the Teaching Gap describe “images of teaching” (see Chapter 3 and Chapter 4). What differences among the three countries were most striking to you?

4) Explain what the authors meant by “content coherence”. Why is this issue important?

5) The Teaching Gap discusses lesson study as a vehicle for improving classroom practice.

a) Provide a brief overview of the attributes and process of lesson study.

b) What is your view of lesson study? Could lesson study be effectively implemented in your school? If so, describe your view of how it could happen, noting any changes to school structure, etc. that would be needed.

6) How did the book make you feel? How did that feeling evolve from beginning to middle to end of the book?

Knowing and Teaching Elementary Mathematics

This book discusses findings from a study by Liping Ma that compares mathematical understanding among U.S. and Chinese elementary school teachers as it relates to classroom teaching practices. A critical finding of the study is that Chinese teachers continue to learn mathematics and to refine their content understandings throughout their teaching careers. Teachers are provided support and time to regularly reflect on and deliberate about their teaching, while U.S. teachers are not. So, please read The Teaching Gap in that spirit -- as an attempt to help us step out of our culture of mathematics teaching in order to examine it more objectively.

1) The preface and chapter 1 of Ma’s book contrast the mathematical knowledge of US teachers and Chinese teachers.

a) What are the primary differences that Ma describes? To what does Ma attribute these differences?

b) What does Ma mean by procedural, conceptual and pseudo conceptual knowledge?

c) What does Ma say about the relationship between teachers’ knowledge and their teaching practices?

d) Compare times when you’ve taught an idea that you understood well with times when you’ve taught an idea that you’ve understood poorly. Were you able to orchestrate more meaningful learning experiences for your students? Explain.

2) Provide a brief overview of Chapter 4, noting especially the differences in the knowledge and attitudes of U.S. and Chinese teachers as they approached their teaching of a novel topic.

3) a) What does Ma mean by “Profound Understanding of Fundamental Mathematics” (PFUM; See Chapter 5).

b) Pick a topic that you understand well. Describe what a profound understanding of it looks like.